Actually, if he was to run it through the back of the car he would have to negotiate all of the modified suspension, which, it would appear, that he would like to be able to adjust without setting himself on fire from the exhaust heat.
And secondly, yes the torque arm does hang down but if he was to run the exhaust pipes out through the side, THEY would now be the lowest part of the car since the exhaust would have to be routed under the subframe connectors.
That wing and nose setup is very common in AIX racing, it looks crude, but it does work. I'm sure that this guy runs some from of heater insulation over the pipes.
I was looking at running through the car headers on a mustang and decided that would be way too much heat to try and control, this setup might be a decent compromise.
BTW: AIX series
YouTube - 2007 American Iron Extreme Finals - Part 2

photgraphic proof that mustangs can also turn corners.